Question

A ray enters a glass sphere of R. I. n = $\sqrt { 3 }$ at an angle of incidence 60° and is reflected and refracted at the farther surface of the sphere. The angle between the reflected and refracted rays at this surface is

• A. 50⁰
• B. 60⁰
• C. 90⁰
• D. 40⁰

Answer 1

Answer: (C)

90⁰

Answer 2

Refraction at P.

$\frac { \operatorname { Sin } 60 ^ { \circ } } { \operatorname { Sin } r _ { 1 } } = \sqrt { 3 }$

⇒

⇒ r₁ = 30⁰

Since r₂ = r₁

∴ r₂ = 30⁰

Refraction at Q $\frac { \operatorname { Sin } r _ { 2 } } { \operatorname { Sin } i _ { 2 } } = \frac { 1 } { \sqrt { 3 } }$ Putting r₂= 30⁰ we obtain i₂ = 60⁰

Reflection at Q

∴ $\alpha = 180 ^ { \circ } - \left( r _ { 2 } ^ { \prime } + i _ { 2 } \right)$

= 180⁰- (30⁰+60⁰) = 90⁰